Locally Indecomposable Galois Representations
Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 277-297

Voir la notice de l'article provenant de la source Cambridge University Press

In a previous paper the authors showed that, under some technical conditions, the local Galois representations attached to the members of a non- $\text{CM}$ family of ordinary cusp forms are indecomposable for all except possibly finitely many members of the family. In this paper we use deformation theoretic methods to give examples of non- $\text{CM}$ families for which every classical member of weight at least two has a locally indecomposable Galois representation.
DOI : 10.4153/CJM-2010-084-3
Mots-clés : 11F80
Ghate, Eknath; Vatsal, Vinayak. Locally Indecomposable Galois Representations. Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 277-297. doi: 10.4153/CJM-2010-084-3
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[Böc99] [Böc99] Böckle, G., Explicit universal deformations of even Galois representations. Math. Nachr. 206(1999), 85–110. Google Scholar

[BM89] [BM89] Boston, N. and Mazur, B., Explicit universal deformations of Galois representations. In: Algebraic number theory, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989, pp. 1–21. Google Scholar

[Cal06] [Cal06] Calegari, F., Eisenstein deformation rings. Compos. Math. 142(2006), no. 1, pp. 63–83. doi:10.1112/S0010437X05001661 Google Scholar

[Fla92] [Fla92] Flach, M., A finiteness theorem for the symmetric square of an elliptic curve. Invent Math. 109(1992), no. 2, 307–327. doi:10.1007/BF01232029 Google Scholar

[GV04] [GV04] Ghate, E. and Vatsal, V., On the local behaviour of ordinary ¤-adic representations. Ann. Inst. Fourier (Grenoble) 54(2004), no. 7, 2143–2162. Google Scholar

[Gha05] [Gha05] Ghate, E., Ordinary forms and their local Galois representations. In: Algebra and number theory, Hindustan Book Agency, Delhi, 2005, pp. 226–242. Google Scholar

[Gou97] [Gou97] Gouvêa, F., Non-ordinary primes: a story. Experiment. Math. 6(1997), no. 3, 195–205. Google Scholar

[Gre91] [Gre91] Greenberg, R., Iwasawa theory for motives. In: L-functions and arithmetic (Durham, 1989), London Math. Soc. Lecture Note Ser., 153, Cambridge Univ. Press, Cambridge, 1991, pp. 211–233. Google Scholar

[Gro90] [Gro90] Gross, B. H., A tameness criterion for Galois representations associated to modular forms (mod p). Duke. Math. J. 61(1990), no. 2, 445–517. doi:10.1215/S0012-7094-90-06119-8 Google Scholar

[Hid86] [Hid86] Hida, H., Galois representations into GL2( p[[X]]) attached to ordinary cusp forms. Invent. Math. 85(1986), no. 3, 545–613. doi:10.1007/BF01390329 Google Scholar

[Maz89] [Maz89] Mazur, B., Deforming Galois representations. In: Galois groups over Q (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., 16, Springer, New York, 1989, pp. 385–437. Google Scholar

[M W86] [M W86] Mazur, B. and Wiles, A., On p-adic analytic families of Galois representations. Compositio Math. 59(1986), 231–264. Google Scholar

[Oht06] [Oht06] Ohtani, S., Deformations of locally abelian Galois representations and unramified extensions. J. Number Theory 120(2006), no. 2, 272–286. doi:10.1016/j.jnt.2005.12.002 Google Scholar

[Rib76] [Rib76] Ribet, K., A modular construction of unramified p-extensions of Q(μp). Invent. Math. 34(1976), no. 3, 151–162. doi:10.1007/BF01403065 Google Scholar

[Ser73] [Ser73] Serre, J.-P., Congruences et formes modulaires [d’après H. P. F. Swinnerton-Dyer]. Séminaire Bourbaki (1971/1972), 416, Lecture Notes in Mathematics, 317, Springer, Berlin, 1973, pp. 319–338. Google Scholar

[Ser89] [Ser89] Serre, J.-P., Abelian l-adic representations and elliptic curves. Second ed., Advanced Book Classics, Addison-Wesley Publishing Company, Redwood City, CA, 1989. Google Scholar

[Was96] [Was96] Washington, L., Introduction to cyclotomic fields. Second ed., Springer-Verlag, Berlin-New York, 1996. Google Scholar

[Wes04] [Wes04] Weston, T., Unobstructed modular deformation problems. Amer. J. Math. 126(2004), no. 6, 1237–1252. doi:10.1353/ajm.2004.0052 Google Scholar

[Wil88] [Wil88] Wiles, A., On ordinary .-adic representations associated to modular forms. Invent. Math. 94(1988), no. 3, 529–573. doi:10.1007/BF01394275 Google Scholar

[Yam04] [Yam04] Yamagami, A., On the unobstructedness of the deformation problems of residual modular representations. Tokyo J. Math. 27(2004), no. 2, 443–455. doi:10.3836/tjm/1244208400 Google Scholar

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